Herman-Wallis Coefficients Research Articles

Cavity ring-down spectroscopy of acetylene near [formula omitted]

A continuous-wave cavity ring-down spectrometer was employed to record the spectrum of the acetylene molecule spanning the 12350 - 12790 cm−1 region. A total of 747 lines from the principal isotopologue and 68 lines from 12C13CH2 were identified, with nearly all line intensities retrieved from the spectra. These lines belong to eighteen vibrational bands of 12C2H2 and two vibrational bands of 12C13CH2, among which five vibrational bands are reported here for the first time. Spectroscopic constants were deduced for all the identified bands, and the vibrational dipole moment squared along with Herman–Wallis coefficients were determined for the majority of these bands. Additionally, several resonance interactions were thoroughly explored.

New acetylene line list near 3.8-μm - Part III - 12C13CH2 and 12C2HD

The intensities of minor acetylene isotopologues 12C13CH2 and 12C2HD have been studied from Fourier transform spectra of acetylene in natural abundance using high optical path length. This study completes the work performed in the two first paper of the series (JQSRT 2023;295:108,413 and JQSRT 2023;311:108,771) where 71 bands of 12C2H2 were studied in the ΔP = 4 spectral region (∼2400–2900 cm−1). In this work, 692 measured line intensities allowed to derive vibrational transition dipole moment squared (and sometimes Herman-Wallis coefficients) for 11 bands of 12C13CH2 and 6 bands of 12C2HD. Using line positions and broadening parameters from literature, a line list has been generated for atmospheric and astrophysical applications.

Elucidating Λ-doublet splittings and rotational quantum number-dependent collisional broadenings in 2∏1/2 and 2∏3/2 spin-split sub-bands of NO at 5.2 µm

High-resolution ro-vibrational spectroscopic features of nitric oxide (NO) are particularly interesting because of the unpaired electron and non-zero nuclear spin of the nitrogen atom. Here, ultra-sensitive cavity ring-down spectroscopy (CRDS) coupled with an external-cavity quantum cascade laser (EC-QCL) radiation source was employed to measure the rotationally-resolved fine structure Λ-doublet splittings between the parity doublet e and f components in the (2∏1/2 - 2∏1/2) and (2∏3/2 - 2∏3/2) allowed sub-bands of the v = 1 ← 0 fundamental vibrational band of NO molecule near 5.2 µm. Subsequently, we determined several principal spectroscopic parameters such as the Λ-doubling constants, vibrational transition dipole moments and the Herman-Wallis coefficients for both e and f Λ-doublet components by probing various R-branch rotational lines (J = 0.5 to 23.5) of the studied spin-split sub-bands of NO associated with spin–orbit interaction. In addition, we performed the pressure broadening effect on the Λ-doublet splittings in collision with three vital perturbing gases at room temperature (296 K) and accurately determined the pressure broadening coefficients, γi (e,f) in cm-1atm−1 [(i = He, Ar and Zero air (mainly N2 + O2)] along with their dependence on the rotational quantum number (J). We observed the pronounced collision-induced rotational quantum effect and the result of rotationally inelastic collision in the system for each collision partner. All these measured high-resolution new spectroscopic parameters over 33 ro-vibrational transitions via an EC-QCL based CRDS method will help significantly in interpreting fundamental molecular properties of this diatomic NO molecule.

Line-by-line intensity measurements of methyl fluoride in the ν2 and ν5 bands

Systematic measurements of line intensities in the ν2 and ν5 bands of CH3F were performed for the first time for 2040 transitions using a mono-spectrum fitting technique utilizing a Voigt and Rautian profiles. The spectra are recorded at room temperature for eight pressures of CH3F from 0.1247 to 2.5080 Torr using the Bruker IFS125HR Fourier Transform spectrometer located at the LISA facility in Créteil. Strong intensity perturbations were observed and analyzed accounting for the strong Coriolis coupling ν2 and ν5 bands and l-type interactions in the ν5 band. The transition dipole moments squared were determined for each line, allowing determination of the vibrational transition moment and the Herman–Wallis coefficients of each band using the Aliev and Watson models. Comparison with data available in the literature permits to test the validity of these models applied to the ν2/ν5 dyad system strongly affected by resonances.

Line intensity parameters, He-broadening and line shift coefficients in the 2v 2 0 and 3v 2 1 − v 2 1 bands of OCS

Using Fourier transform spectrometer, He-broadening coefficients in the and bands of carbonyl sulfide (16O12C32S) have been measured for the first time in the P- and R-branches. Measurements have been performed at room temperature (295 K) for 200 ro-vibrational lines with rotational quantum number ranging from 1 ≤ J ≤ 64, using a mono-spectrum non-linear least squares fitting of Voigt profiles. The measured values were discussed as a function of the rotational quantum number and compared to previous data. These broadening coefficients were also calculated on the basis of Robert and Bonamy's formalism using an ab-initio potential energy surface (PES). In addition, we have measured pressure shift coefficients for 92 transitions in both bands, these results were compared with those of the 2ν3 band. The line intensities in the and bands were also retrieved using the same spectra. The analysis of these intensities allows us to derive a consistent set of line intensity parameters such as vibrational transition moments, band intensities as well as Herman-Wallis (HW) coefficients.

Theory of rovibrational line intensities in allowed and collision-induced absorption spectra of linear molecules

A theoretical approach is developed for the Herman-Wallis factors describing the variation of the line intensities caused by rovibrational interaction in a linear molecule. In the case of ${\ensuremath{\nu}}_{2}$ and ${\ensuremath{\nu}}_{3}$ fundamentals and the ${\ensuremath{\nu}}_{1}+{\ensuremath{\nu}}_{3}/2{\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{3}$ resonance combination band in a ${\mathrm{CO}}_{2}$ molecule, our theory is capable of generating reliable numerical estimates for the linear Herman-Wallis coefficients without recourse to complicated algebra. On the assumption of nearly free rotating monomers, an analog of the Herman-Wallis factors is introduced for the dipole-forbidden ${\ensuremath{\nu}}_{2}+{\ensuremath{\nu}}_{3}$ band, which manifests itself in ${\mathrm{CO}}_{2}$ collision-induced absorption (CIA). The rovibrational perturbation is appropriate to explain a pronounced crossflow of intensity among rovibrational branches in a virtually rotationally unresolved CIA envelope.

Line intensities and self-broadening coefficients of CH3I in the region of ν5 and ν3+ν6 bands

Systematic measurements of self-broadening coefficients for 992 transitions in the ν5 and ν3+ν6 perpendicular bands of CH3I up to the quantum numbers 3 ≤ J ≤ 52 and 0 ≤ K ≤ 12 have been performed for the first time using a mono-spectrum fitting technique utilizing a Voigt profile. Our previous line intensity measurements [Boughdiri, et al., JQSRT 221 (2018) 147-154] are also extended using new spectra recorded at room temperature at five pressures from 1.15 to 9.98 mbar using the Bruker IFS125HR Fourier Transform spectrometer at the AILES beamline of the SOLEIL Synchrotron facility. The measured absolute intensities were used to derive the transition dipole moment squared for each line, the band intensities as well as the Herman–Wallis coefficients. The rotational dependences of the self-broadening coefficients have been clearly observed and modeled. The data were compared with previous works. The results are given as supplementary data table for a possible use in atmospheric and industrial applications.

High sensitivity absorption spectroscopy of acetylene near 1.2 µm

The weak high-resolution absorption spectrum of natural acetylene has been recorded by high sensitivity cavity ring down spectroscopy (CRDS) near 1.2 µm. The frequency scale of the spectra was obtained by coupling the CRDS spectrometer to a self-referenced frequency comb. The room temperature recordings, performed at a pressure of 10.0 Torr, cover the 8210–8670 cm−1 spectral interval. A list of more than 11,000 lines was constructed in the region. The smallest intensity values are on the order of 10−29 cm/molecule which is more than two orders of magnitude smaller than previous measurements by Fourier transform spectroscopy (FTS). More than 2600 lines were rovibrationally assigned using previous observations and predictions based on the effective operator approach. They include 2270, 338 and 28 absorption lines of 12C2H2, 12C13CH2 and 12C2HD, respectively, belonging to a total of 52 vibrational bands, thirty-six of them being newly reported. For comparison, the HITRAN2016 database provides line parameters of only two 12C2H2 bands, in the same region. Spectroscopic parameters of the upper vibrational levels were derived from standard band-by-band fits of the line positions (typical rms values of the (obs.-calc.) deviations are better than 0.002 cm–1). The vibrational transition dipole moment squared and Herman-Wallis coefficients of 39 bands were derived from a fit of the intensity values measured in this work and combined with previous FTS data for the strongest bands. A recommended list is constructed in the region using calculated line parameters for the unperturbed bands and experimental positions and intensities for the others. The recommended list including a total of 3139 transitions will help to complete acetylene spectroscopic databases in the near-infrared.

Measurements of Line Intensities and Self-broadening Coefficients in the ν2 Band of CH3I

The line intensities and pressure broadening coefficients for transitions in the three branches of the ν2 parallel band of CH3I are measured for the first time for about 1317 lines with rotational quantum numbers 2 ≤ J ≤ 70 and 0 ≤ K ≤ 13 using a mono-spectrum fitting technique utilizing a Voigt profile. Five spectra have been recorded at room temperature (T = 297.6 K) with a high resolution Fourier transform spectrometer at pressures between 1.15 and 9.98 mbar. The measured intensities were used to derive the transition dipole moment squared for each line, the band intensity as well as the Herman–Wallis coefficients. These parameters were used to predict the values of line intensities. The band intensity was compared with previous works performed at medium resolution. The rotational dependencies of the self-broadening coefficients have been clearly observed and modeled using an empirical model. The average accuracies were estimated to be around 5 % for line intensities and self-broadening coefficients.The whole set of results is given as supplementary material for a possible use in atmospheric and industrial applications.

The acetylene spectrum in the 1.45 µm window (6627–7065 cm–1)

The high-resolution absorption spectrum of acetylene has been recorded at room temperature by high sensitivity cavity ring down spectroscopy (CRDS) in the 6627–7065 cm–1 region. The studied spectral range corresponds to a spectral interval of very weak absorption (an acetylene transparency window). The positions and intensities of more than 6500 lines are determined in the considered interval where previous intensity information was mostly missing. On the basis of previous studies and on effective Hamiltonian predictions, 3062 12C2H2, 462 12C13CH2 and 104 12C2HD absorption lines belonging to a total of 123 vibrational bands are assigned. For comparison, the HITRAN2016 database provides line parameters of only ten 12C2H2 bands in the same region. Spectroscopic parameters of 113 upper vibrational levels were derived from standard band-by-band fits of the line positions (typical rms values of the (obs.-calc.) deviations are better than 0.003 cm–1). Many bands are found to be affected by perturbations. The vibrational transition dipole moment squared and Herman-Wallis coefficients of 47 bands were derived from a fit of the measured intensity values. In order to generate a recommended line list in the region, the derived spectroscopic parameters and Herman-Wallis coefficients were used to compute the line parameters for these 47 bands while experimental position and intensity values were kept for the other bands. Overall, the obtained recommended list including a total of 5260 transitions will help to fill a spectral gap around 1.47 µm where very scarce spectroscopic information is provided in the current spectroscopic databases. When compared to the HITRAN list in the region, some important deviations concerning both line positions and line intensities are evidenced as a result of inaccurate high J extrapolations.

Line intensity parameters in the ν3 and 2ν3-ν3 bands of methyl chloride in the 13 µm region

We performed the systematic measurements of line intensities of ro-vibrational absorption transitions of the ν3 and 2ν3-ν3 parallel bands of 12CH335Cl and 12CH337Cl isotopes. The spectra were recorded in the spectral region between 650 and 800 cm−1 with a high-resolution Fourier transform spectrometer.A mono-spectrum fitting technique was used to fit a series of seven spectra at pressures of CH3Cl ranging from 1.02 to 10.24 mbar to retrieve line intensities of 2385 transitions of the two isotopic species. The measured line intensities are discussed in relation to rotational quantum numbers, and used to derive the square of the transition dipole moments for each line. The analysis of these moments allows us to derive a consistent set of line intensity parameters, such as vibrational transition moments, band intensities as well as Herman-Wallis coefficients for both bands. The results of the ν3 band are in satisfactory agreement with previous works and present databases, but a larger discrepancy (≈ 30%) is observed for the 2ν3-ν3 hot band.

High-resolution cw-cavity ring-down spectroscopy of allowed (ν4 + ν5)0 and forbidden (ν4 + ν5)2 bands of C2H2 using external-cavity quantum cascade laser

In this paper, we measured the absolute line intensities and air broadening coefficients of several rotationally resolved lines in the P and R branches of the allowed (ν4 + ν5)0 and forbidden (ν4 + ν5)2 vibrational combinational bands of C2H2 at room temperature 296 K. These measurements were performed using an external-cavity quantum cascade laser (EC-QCL) operating at 7.5 μm coupled with high-sensitive cavity ring-down spectroscopy (CRDS). Rotational level-dependent pressure-broadening coefficients of the resolved spectral lines of the selected transitions from (ν4 + ν5)0 band are reported here. The air broadening coefficients for 5 rotational lines from P-branch of (ν4 + ν5)2 band were also obtained first time with better than 3% uncertainty. The vibrational transition dipole moment squared values of the rotational lines and empirical Herman-Wallis coefficients were also quantified from experimental data. Finally, experimentally obtained all spectroscopic parameters were rigorously compared with previous studies. The new experimental data including several spectroscopic parameters will be useful for atmospheric and astrophysics applications.

Line intensities and self-broadening coefficients of methyl chloride in the 10 µm region

We performed the first systematic measurements of line intensities and pressure broadening coefficients of ro-vibrational absorption transitions of the ν6 perpendicular band of CH335Cl and CH337Cl isotopologues. The spectra were recorded in the spectral region between 920 and 1130 cm−1 with a high-resolution Fourier transform spectrometer. A multi-pressure fitting technique was used to fit a series of seven spectra at pressures of CH3Cl ranging from 1.02 to 10.24 mbar to derive these parameters for about 2132 transitions with 1 ≤ J ≤ 55 and 0 ≤ K ≤ 12. The line intensities were discussed as a function of the rotational quantum numbers, and were used to derive the transition dipole moments squared for each line. The analysis of these moments allows us to derive a consistent set of line intensity parameters such as vibrational transition moments, band intensity as well as Herman-Wallis coefficients. The results were found to be in satisfactory agreement with databases and with low resolution measurements of band intensity.The rotational dependencies of the self-broadening coefficients have been clearly observed and modeled using an empirical polynomial law. The average accuracies have been estimated to be around 4 and 5% for line intensities and self-broadening coefficients respectively.

The CRDS spectrum of acetylene near 1.73 µm

The high-resolution absorption spectrum of acetylene has been recorded at room temperature by high sensitivity cavity ring down spectroscopy (CRDS) in the 5693–5882 cm–1 region. The noise level of the recordings corresponds to a typical minimum detectable absorption, αmin, below 10-10 cm−1. The positions and intensities of about 4000 lines were determined and analyzed together with about 3900 lines left unassigned in a previous CRDS study in the 5850–6340 cm−1 region. In total, about 2620 12C2H2 and 250 12C13CH2 absorption lines are assigned in the present work, most of them being newly reported. The 12C2H2 lines belong to 53 bands and include 24 bands newly identified or improved in the region of the previous study. Altogether, 107 bands in the entire 5693–6340 cm−1 while the HITRAN database provides line parameters of only nine 12C2H2 bands in the same region. The lines of 12C13CH2 in normal abundance (2.2%) belong to eight bands whose intensities are reported for the first time. Spectroscopic parameters of the upper vibrational levels were derived from standard band-by-band fits of the line positions (typical rms values of the (obs.-calc.) deviations are better than 0.002 cm–1). The vibrational transition dipole moment squared and Herman–Wallis coefficients of each band were derived from a fit of the measured intensity values. A recommended line list is provided for the bands newly assigned with positions calculated using empirical spectroscopic parameters of the lower and upper energy vibrational levels and intensities computed using the derived Herman–Wallis coefficients. As a result, the constructed line list includes a total of 4471 transitions belonging to 53 bands of 12C2H2 and 8 bands of 12C13CH2. This list of acetylene transitions above 5693 cm−1 extends to lower energy and completes our empirical spectroscopic database for acetylene in the 5850–9415 cm−1 range.

The absorption spectrum of acetylene near 1 µm (9280–10,740 cm-1) (II): Line intensities

In a companion paper, rovibrational assignments of acetylene in the 9280–10,740 cm–1 region were extended on the basis of a long path absorption spectrum recorded by Fourier-transform spectroscopy. Thirty-three and seven bands of 12C2H2 and 12C13CH2 were assigned, respectively, twelve 12C2H2 bands being newly assigned. In the present work, the vibrational transition dipole moments squared and Herman–Wallis coefficients of the bands are derived from a fit of the measured intensity values. An empirical recommended line list is provided with positions calculated using empirical spectroscopic band parameters and intensities calculated using the derived Herman–Wallis coefficients. As a result the constructed line list in the 9450–10,740 cm-1 region includes a total of 2774 lines belonging to 32 bands of 12C2H2 and seven bands of 12C13CH2. For comparison the HITRAN database in the same region includes 305 lines of 4 bands, all belonging to 12C2H2. The recommended acetylene line list is compared to the HITRAN line list and to the Acetylene Spectroscopic Database (ASD) constructed using the global effective operator approach.The measured bands belong to the ΔP = 15 and 16 series of bands where P = 5V1 + 3V2 + 5V3 + V4 + V5 is the polyad quantum number. An improved set of ΔP = 15 effective dipole moment (EDM) parameters is derived from a fit of the measured intensity values. The ΔP = 16 EDM parameters are derived for the first time. The derived sets of EDM will allow extending the Acetylene Spectroscopic Database at higher energy.

An empirical spectroscopic database for acetylene in the regions of 5850–6341 cm−1 and 7000–9415 cm−1

Six studies have been recently devoted to a systematic analysis of the high-resolution near infrared absorption spectrum of acetylene recorded by Cavity Ring Down spectroscopy (CRDS) in Grenoble and by Fourier-transform spectroscopy (FTS) in Brussels and Hefei. On the basis of these works, in the present contribution, we construct an empirical database for acetylene in the 5850–9415cm–1 region excluding the 6341–7000cm−1 interval corresponding to the very strong ν1+ν3 manifold. Our database gathers and extends information included in our CRDS and FTS studies. In particular, the intensities of about 1700 lines measured by CRDS in the 7244–7920cm−1 region are reported for the first time together with those of several bands of 12C13CH2 present in natural isotopic abundance in the acetylene sample.The Herman-Wallis coefficients of most of the bands are derived from a fit of the measured intensity values. A recommended line list is provided with positions calculated using empirical spectroscopic parameters of the lower and upper energy vibrational levels and intensities calculated using the derived Herman-Wallis coefficients. This approach allows completing the experimental list by adding missing lines and improving poorly determined positions and intensities. As a result the constructed line list includes a total of 11113 transitions belonging to 150 bands of 12C2H2 and 29 bands of 12C13CH2. For comparison the HITRAN database in the same region includes 869 transitions of 14 bands, all belonging to 12C2H2. Our weakest lines have an intensity on the order of 10–29cm/molecule, about three orders of magnitude smaller than the HITRAN intensity cut off. Line profile parameters are added to the line list which is provided in HITRAN format.The comparison of the acetylene database to the HITRAN2012 line list or to results obtained using the global effective operator approach is discussed in terms of completeness and accuracy.

Line intensity measurements for acetylene between 8980 and 9420 cm–1

The absorption spectrum of acetylene is studied by high-resolution Fourier-transform spectroscopy (FTS) between 8980 and 9420cm–1. Positions and intensities of 432 12C2H2 absorption lines are retrieved from a spectrum recorded at room temperature (298.5K) with a pressure of 87.6hPa and a 105m path length. The measured lines belong to 11 bands including three bands observed for the first time. The obtained intensity dataset constitutes the first intensity information in the region. The Herman-Wallis coefficients are derived from a fit of the measured intensity values. The reported results will be valuable to complete the spectroscopic databases of acetylene.

High sensitivity cavity ring down spectroscopy of 13C16O2 overtone bands near 806 nm

The absorption spectrum of 13C16O2 near 806nm has been recorded with a continuous-wave cavity ring-down spectrometer. Two cold bands and one associated hot band are observed in this region. The line positions of these bands are determined with an accuracy of 0.003cm−1. The absolute line intensities have also been retrieved with an estimated accuracy of 4% for majority of the unblended lines. The vibrational transition dipole moment squared values and the empirical Herman–Wallis coefficients are determined for all the three bands. The comparison of the retrieved line positions and intensities to those given in the Carbon Dioxide Spectroscopic Databank shows large deviations in the line intensities of the 10052–00001 band. The effective dipole moment parameters describing the line intensities of 13C16O2 near 806nm are fitted according to the observed line intensities.

Spectral line parameters including temperature dependences of air-broadening for the 2 ← 0 bands of 13C16O and 12C18O at 2.3 μm

The first air broadening line shape parameters were determined for the 2←0 bands of 13C16O near 4166.8cm−1 and 12C18O near 4159.0cm−1. Air-broadened Lorentz half-width coefficients, their temperature dependence exponents; air-induced pressure shift coefficients, their temperature dependences; and air line mixing coefficients were measured. Additionally, speed-dependent line shapes with line mixing employing the off-diagonal relaxation matrix element coefficients were applied to minimize the fit residuals. Finally, individual line positions and line intensities of the two isotopologues were constrained to the well-known theoretical quantum mechanical expressions in order to obtain the rovibrational (G, B, D and H) and band intensity parameters (including Herman–Wallis coefficients). For this, laboratory spectra were recorded at 0.005cm−1 resolution using a temperature-controlled coolable absorption cell configured inside a Bruker IFS 125HR Fourier transform spectrometer. Gas temperatures and pressures for the spectra varied from 150 to 298K and 20 to 700Torr, respectively. Results were obtained from broad-band multispectrum least-squares fitting of the 4000–4360cm−1 spectral region. Four isotope-enriched pure sample spectra and twelve spectra with air+CO samples (13C16O or 12C18O, as appropriate) were fitted simultaneously. The results obtained for 13C16O and 12C18O are compared and discussed.

Spectral line parameters including temperature dependences of self- and air-broadening in the 2←0 band of CO at 2.3 μm

Temperature dependences of pressure-broadened half-width and pressure-induced shift coefficients along with accurate positions and intensities have been determined for transitions in the 2←0 band of 12C16O from analyzing high-resolution and high signal-to-noise spectra recorded with two different Fourier transform spectrometers. A total of 28 spectra, 16 self-broadened and 12 air-broadened, recorded using high-purity (≥99.5% 12C-enriched) CO samples and CO diluted with dry air (research grade) at different temperatures and pressures, were analyzed simultaneously to maximize the accuracy of the retrieved parameters. The sample temperatures ranged from 150 to 298K and the total pressures varied between 5 and 700Torr. A multispectrum nonlinear least squares spectrum fitting technique was used to adjust the rovibrational constants (G, B, D, etc.) and intensity parameters (including Herman–Wallis coefficients), rather than determining individual line positions and intensities. Self- and air-broadened Lorentz half-width coefficients, their temperature dependence exponents, self- and air-pressure-induced shift coefficients, their temperature dependences, self- and air- line mixing coefficients, their temperature dependences and speed dependence have been retrieved from the analysis. Speed-dependent line shapes with line mixing employing off-diagonal relaxation matrix element formalism were needed to minimize the fit residuals. This study presents a precise and complete set of spectral line parameters that consistently reproduce the spectrum of carbon monoxide over terrestrial atmospheric conditions.